Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1?
A)
(1,0)


cross out

B)
(−2,2)


cross out

C)
(1,6)


cross out

D)
(0,1)


cross out

E)
(1,4)


cross out

F)
(−2,7)

Step-by-step explanation:

I think you mean the sun's mass is 1.99 × 10³⁰ kg.

70% of that is hydrogen :

1.99 × 10³⁰ × 0.7 = 1.393 × 10³⁰ kg

a.

13% of that is in the core :

1.393 × 10³⁰ × 0.13 = 0.18109 × 10³⁰ = 1.8109 × 10²⁹ kg

b.

600 000 000 000 kg = 6.0 × 10¹¹ kg/s

so, 1.8109 × 10²⁹ kg will last

1.8109 × 10²⁹ / (6.0 × 10¹¹) = 0.301816666... × 10¹⁸ =

= 3.01816666... × 10¹⁷ seconds

60 seconds per minute.

60 minutes per hour.

24 hours per day.

365 days per year.

1 000 000 000 years.

that is

31,536,000,000,000,000 seconds in 1 billion years =

= 3.1536 × 10¹⁶ seconds in 1 billion years

so, this will go on for

3.018166666... × 10¹⁷ / 3.1536 × 10¹⁶ billion years =

= 0.957054372... × 10¹ = 9.57054372... billion years.

c.

the sun has already "spent" 4.6 billion years, so, that leaves about

9.6 - 4.6 = 5 billion years

According to the information, the total mass of hydrogen available for nuclear fusion in the Sun's core is 10^29 kg, the duration of the oroginal supply of hydrogen of the sun is 3.02 × 10^17 seconds, and the left time of the sun is 4.98 billion years.

a. The total mass of hydrogen available for nuclear fusion in the Sun's core is:

0.7 × 1.99 × 10^30 kg × 0.13 = 1.81 × 10^29 kg

How long the sun's original suply of hydrogen can last?

t = (1.81 × 10^29 kg) / (6 × 10^11 kg/s) = 3.02 × 10^17 seconds

Converting to billions of years:

t = (3.02 × 10^17 s) / (3.15 × 10^16 s/billion years) = 9.58 billion years

c. The Sun has already burned for 4.6 billion years, so the amount of time it has left before it runs out of fuel is:

9.58 billion years - 4.6 billion years = 4.98 billion years

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Answer:{y,x}={-4,-1}

Step-by-step explanation:

Answer:

its 112.7

Step-by-step explanation:

x+2x=3x. 3x = 338

divide 3x and 338 by 3 three is cancelled and x equals to 112.7

[tex]\sf x=13.[/tex]

Assuming that the canvas has a standard rectangle shape, the area should be given by: [tex]\sf A= bh[/tex], where "b" is the base length of the rectangle, and "h" its heignt.

We're told that the canvas is "x" inches wide, and that the length of it is "twice as long as the width", thus it is "2x". Now, let's take width as the base, and length as the height.

Since the formula for area is just a product between width and length, and those values are "x" and "2x", respectively, the formula for the area of this canvas is:

[tex]\sf (x)(2x)=338(in^{2} )[/tex]

a) Solve the product.

[tex]\sf (x)(2x)=338(in^{2} )\\ \\\sf 2x^{2} =338(in^{2} )[/tex]

b) Divide by "2" on both sides of the equation.

[tex]\sf \dfrac{2x^{2}}{2} =\dfrac{338(in^{2} )}{2} \\ \\x^{2} =169[/tex]

c) Take the square root of both sides.

[tex]\sf \sqrt{x^{2}} =\sqrt{169} \\ \\x=13[/tex]

[tex]\sf x=13.[/tex]

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Answer:

The answer is A.

Step-by-step explanation:

For this graph, you are using the linear equation formula: y = mx + b

Answer:

3π

Step-by-step explanation:

Given

Radius=9

Angle=60°

Since PQ is an arc

Perimeter of an Arc =(θ/360)×2πr

60/360×2π(9)

1/6×18π

3π

The quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.

To solve the above problem, we can use the following equation:

Rice + Milk + Sugar = 1 kg

Rice = 2/5 (1 kg) = 0.4 kg

Milk = 2/5 (1 kg) = 0.4 kg

Sugar = 1/6 (1 kg) = 0.167 kg

Therefore, the quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.

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Answer:

Step-by-step explanation:

To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.

The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.

The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.

Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.

Answer:

N = M + 10/3P

Step-by-step explanation:

i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.

ii. The line graph of the data is illustrated below.

iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.

iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.

For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:

Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1

To find the median, we first need to arrange the data in ascending order:

6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3

Since there are an even number of values, the median is the average of the two middle values:

Median of Company A = (8.0 + 8.5) / 2 = 8.25

For Company B, the sample mean can be calculated similarly:

Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2

Arranging the data in ascending order, we get:

9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1

Since there are an odd number of values, the median is the middle value:

Median of Company B = 10.2

Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.

Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.

To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.

Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:

Difference in means ± (t-value x standard error of difference in means)

The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.

Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:

Margin of Error = 1.734 * 0.393 ≈ 0.682

Finally, we can construct the 90% confidence interval for the difference in means as:

Difference in means ± Margin of Error

Calculating the difference in means (mean of Company B - mean of Company A), we have:

Difference in means = 10.2 - 8.1 = 2.1

Therefore, the 90% confidence interval is:

2.1 ± 0.682

This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.

Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.

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The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.

It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.

Recall; Circumference, C = 2πr

r = C / 2π

r = 50.27 / 2π

r = 8.000718989

Ultimately, the integer which is closest to the radius is; Choice A; 8.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{ 5 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{ 5 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -4 = - \cfrac{ 5 }{ 4 } ( x +4) \\\\\\ y-4=- \cfrac{ 5 }{ 4 }x-5\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 4 }x-1 \end{array}}[/tex]

The horizontal asymptotes of the function is y = 0 and the y-intercepts is (0, 1).

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In this problem, the graph of the function f(x) = (1/4)ˣ is attached below the question and the characteristics of the graph are;

1. The domain of the function is {x|x ∈ R}

2. The range of the function is {y|y > 0}

3. The horizontal asymptotes is y = 0

4. The x-intercepts does not exists

5. The y-intercepts are (0, 1)

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There was no error in the procedure as we can see below.

In algebra, a formula expresses a relationship between two or more variables. Changing the subject of a formula means isolating a specific variable on one side of the equation. This is done by applying inverse operations in a specific order to eliminate all other variables and isolate the desired one.

We have the formula as;

[tex]A = \pi R^2 - \pi r^2\\A = \pi(R^2 - r^2)\\A/ \pi = R^2 - r^2\\R^2 = A/ \pi + r^2\\R = \sqrt{} A/ \pi + √r^2\\R = \sqrt{} A/ \pi + r[/tex]

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The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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Answer:

9 belongs to set N, natural, whole, integer, rational, and real number

Step-by-step explanation:

* Natural number: use for counting

* Whole number: includes natural number and zero

* Integer : are whole numbers and their opposite

*Rational number:come from fraction, and their results can be positive integer

*Real number: includes all numbers

The exact values for both equations are as follows:

a) 3

b) -√3/2 - √2/2

a) In order to ascertain the precise value of 4sin(π/6) + tan(π/4), we must first evaluate the trigonometric functions involved: sin(π/6) = 1/2 and tan(π/4) = 1.

Now, by substituting these values in the equation, we get

4(1/2) + 1 = 2 + 1 = 3.

b) To calculate cos(4π/3) tan(330°) - sin(3π/4), it is necessary to convert 330° into radians: (330 * π) / 180 = 11π/6.

After setting this conversion, evaluate the trigonometric functions present: cos(4π/3) = -1/2, tan(11π/6) = √3, and sin(3π/4) = √2/2.

When these values are used within the equation, the result is (-1/2)(√3) - (√2/2) which equals -√3/2 - √2/2.

Ergo, the exact values for both equations are as follows:

a) 3

b) -√3/2 - √2/2

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(a) The domain of f of g is {1, 8}.

(b) The range of f of g is {0, 1}.

The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.

(a) Domain of f of g:

The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.

To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.

(b) Range of f of g:

The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.

We have:

f(g(1)) = f(8) = 0

f(g(4)) = f(2) = 1

f(g(8)) = f(0) = 1

Therefore, the range of f of g is {0, 1}.

Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.

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The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.

Given: cosθ = -1/3 and θ is in quadrant III.

This means that sinθ = ± √(1 - (cosθ)2).

We know that cosθ is negative, so sinθ will be negative.

Therefore, sinθ = -√(1 - (-1/3)2 )

sinθ = - √(1 - 1/9)

sinθ = -√8/9

tanθ = sinθ/cosθ

tanθ = (-√8/9)/-1/3

tanθ = √8/3

secθ = 1/cosθ

secθ = 1/-1/3

secθ = -3

cscθ = 1/sinθ

cscθ = 1/-√8/9

cscθ = -√9/8

cotθ = cosθ/sinθ

cotθ = -1/3/-√8/9

cotθ = √9/8

Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.

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Answer:

Step-by-step explanation:

The use of calculations to show that the height of the barrel of oil is 96.82cm is given below:

The volume is given as V = 42 gal

The radius is given as r = 18/2 = 9 in

The height is given as h= 96.83 cm

Using the formula:

V = πr²h

h = V/(πr²)

The volume is given as V = 42 gal

42 gal x 3.7854 l/gal = 158.987 l

158.987 l = 158,987 ml = 158,987 cm³

The radius is given as r = 18/2 = 9 in

9 in x 2.54 cm/in = 22.86 cm

The height is given as h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm

depending on how you round, the more precise answer is 96.8285 ≈ 96.83 cm

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Answer:

x+y=9

5x+8y=66

Step-by-step explanation:

The sum of both numbers is 107/12

One number is 6 3/4

The other smaller number is 2 1/6

The sum of both numbers can be calculated as follows

= 6 3/4 + 2 1/6

= 27/4 + 13/6

= 162 + 52/24

= 214/24

= 107/12

Hence the sum of both numbers is 107/12

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the rate of interest is 11.25%.we can use simple interest formula get answer as above

what is simple interest ?

Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.

In the given question,

We can use the formula for simple interest to solve for the rate:

Simple Interest = (Principal x Rate x Time) / 100

Substituting the given values, we get:

$900 = (400 x Rate x 20) / 100

Multiplying both sides by 100 and dividing by 400 x 20, we get:

Rate = $900 / (400 x 20) = 0.1125 or 11.25%

Therefore, the rate of interest is 11.25%.

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the deductible, and the coinsurance. Here are the steps to calculate the total out-of-pocket expense: the total out-of-pocket expense for one month is $ [tex]154[/tex] .

To calculate the out-of-pocket expense for one month, we need to take into account the monthly premium.

Step 1: Calculate the deductible

The deductible is the amount that the insured person needs to pay before the insurance starts covering the costs.

In this case, the deductible is $500 because that's the threshold for the 90% coverage. Since the family will fill 6 prescriptions per month, we need to calculate the average cost per prescription:

Average cost per prescription = Total prescription costs / Number of prescriptions

Average cost per prescription = $ [tex]850 / 6 = $141.67[/tex]

Since the deductible is $500, the insurance will cover 90% of the first $500, which is $450. The remaining $50 will be paid by the insured person. Therefore, the deductible is $  [tex]500 - $450 = $50.[/tex]

Step 2: Calculate the coinsurance

After the deductible is met, the insurance will cover 80% of the remaining prescription costs, and the insured person will be responsible for the remaining  [tex]20[/tex] %.

To calculate the coinsurance, we need to subtract the deductible from the total prescription costs and multiply the result by 0.2:

Coinsurance = (Total prescription costs - Deductible) x 0.2

Coinsurance = [tex]($850 - $500) \times 0.2[/tex]

Coinsurance = $ [tex]70[/tex]

Step 3:

Calculate the total out-of-pocket expense

The total out-of-pocket expense is the sum of the monthly premium, the deductible, and the coinsurance:

Total out-of-pocket expense = Monthly premium + Deductible + Coinsurance

Total out-of-pocket expense = $  [tex]34 + $50 + $70[/tex]

Total out-of-pocket expense = $154

Therefore, the total out-of-pocket expense for one month is $ [tex]154[/tex] .

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This statement describes the relationship between symmetries and rotations

This statement describes a relation between two symmetry operations, denoted by [tex]s_i[/tex] and [tex]s_j[/tex], and a rotation operation denoted by [tex]r_{i-j}[/tex]. The notation [tex]"s_i \circ s_i"[/tex] and [tex]"s_j \circ s_i"[/tex] denotes the composition of these operations, which means applying one operation after the other.

The statement says that [tex]s_i[/tex] and [tex]s_j[/tex] are both symmetries, and that they have a specific relationship with each other: when [tex]s_i[/tex] is composed with itself, it gives the identity operation (denoted by 1), and when [tex]s_j[/tex] is composed with [tex]s_i[/tex], it also gives the identity operation.

Then the statement concludes that this relationship implies that [tex]s_j[/tex] can be obtained by first applying [tex]s_i[/tex] and then applying a rotation operation [tex]r_{i-j}[/tex], and that [tex]s_i[/tex] can be obtained by first applying a rotation operation [tex]r_{i-j}[/tex] and then applying [tex]s_j[/tex].

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The required direction of the inequality is below the line.

If you're not graphing a vertical line, the inequality's sign will tell you which half-plane to shade. Shade above the line when using the  or > sign. Shade below the line if the symbol or is used. Larger solutions are to the right and smaller solutions are to the left, respectively, for a vertical line.

To check the direction, we will take points from the graph and put in the given inequality.

At point (2, 0)

y ≤ x/4 - 3

0 ≤ 2/4 - 3

0 ≤ -25

It is false

Again

At (2, -4)

y ≤ x/4 - 3

-4 ≤ 2/4 - 3

-4 ≤ -2.5

It is true,

Thus, we can say the direction of the inequality is below the line.

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The length of ON for the intersecting secants is derived to be equal to 14

The intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

MK × KL = MO × MN

note that KL = (ON - 3) so;

[13 + (ON - 3)] × 13 = (12 + ON) × 12

13(10 + ON) = 144 + 12ON

130 + 13ON = 144 + 12ON

13ON - 12ON = 144 - 130 {collect like terms}

ON = 14

Therefore, the length of ON for the intersecting secants is derived to be equal to 14

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